{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:DGTZ32VCI5ROXHHI7KQGTBSSR5","short_pith_number":"pith:DGTZ32VC","schema_version":"1.0","canonical_sha256":"19a79deaa24762eb9ce8faa06986528f5c0b0a8927bfb753b0d0d404fe24f58f","source":{"kind":"arxiv","id":"1009.2723","version":1},"attestation_state":"computed","paper":{"title":"Tests of Non-Equivalence among Absolutely Nonsingular Tensors through Geometric Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.OT","authors_text":"Kazumitsu Maehra, Mitsuhiro Miyazaki, Takeshi Sasaki, Toshio Sakata, Toshio Sumi, Yoshitaka Watanabe","submitted_at":"2010-09-14T17:38:36Z","abstract_excerpt":"4x4x3 absolutely nonsingular tensors are characterized by their determinant polynomial. Non-quivalence among absolutely nonsingular tensors with respect to a class of linear transformations, which do not chage the tensor rank,is studied. It is shown theoretically that affine geometric invariants of the constant surface of a determinant polynomial is useful to discriminate non-equivalence among absolutely nonsingular tensors. Also numerical caluculations are presented and these invariants are shown to be useful indeed. For the caluculation of invarinats by 20-spherical design is also commented."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.2723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2010-09-14T17:38:36Z","cross_cats_sorted":[],"title_canon_sha256":"8c8e9ee02ff73fc757f5c20e6484defe8ed6b7d4f91613f45652da265d28d62b","abstract_canon_sha256":"8b61886d0b2d932d0b6e814f4a4cbffa9d357d875ed2a7f85808fe9217ea0b8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:56.483370Z","signature_b64":"kSPe292yrc/fwBF4JqhwooQG9K7omyrRoqZVbKHjVeBmPLzZacIXdi4tJ+rVTOU/T+wNw3SXEiYxH/ZnQlwPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19a79deaa24762eb9ce8faa06986528f5c0b0a8927bfb753b0d0d404fe24f58f","last_reissued_at":"2026-05-18T04:40:56.482717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:56.482717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tests of Non-Equivalence among Absolutely Nonsingular Tensors through Geometric Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.OT","authors_text":"Kazumitsu Maehra, Mitsuhiro Miyazaki, Takeshi Sasaki, Toshio Sakata, Toshio Sumi, Yoshitaka Watanabe","submitted_at":"2010-09-14T17:38:36Z","abstract_excerpt":"4x4x3 absolutely nonsingular tensors are characterized by their determinant polynomial. Non-quivalence among absolutely nonsingular tensors with respect to a class of linear transformations, which do not chage the tensor rank,is studied. It is shown theoretically that affine geometric invariants of the constant surface of a determinant polynomial is useful to discriminate non-equivalence among absolutely nonsingular tensors. Also numerical caluculations are presented and these invariants are shown to be useful indeed. For the caluculation of invarinats by 20-spherical design is also commented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2723","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.2723","created_at":"2026-05-18T04:40:56.482797+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.2723v1","created_at":"2026-05-18T04:40:56.482797+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2723","created_at":"2026-05-18T04:40:56.482797+00:00"},{"alias_kind":"pith_short_12","alias_value":"DGTZ32VCI5RO","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"DGTZ32VCI5ROXHHI","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"DGTZ32VC","created_at":"2026-05-18T12:26:06.534383+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DGTZ32VCI5ROXHHI7KQGTBSSR5","json":"https://pith.science/pith/DGTZ32VCI5ROXHHI7KQGTBSSR5.json","graph_json":"https://pith.science/api/pith-number/DGTZ32VCI5ROXHHI7KQGTBSSR5/graph.json","events_json":"https://pith.science/api/pith-number/DGTZ32VCI5ROXHHI7KQGTBSSR5/events.json","paper":"https://pith.science/paper/DGTZ32VC"},"agent_actions":{"view_html":"https://pith.science/pith/DGTZ32VCI5ROXHHI7KQGTBSSR5","download_json":"https://pith.science/pith/DGTZ32VCI5ROXHHI7KQGTBSSR5.json","view_paper":"https://pith.science/paper/DGTZ32VC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.2723&json=true","fetch_graph":"https://pith.science/api/pith-number/DGTZ32VCI5ROXHHI7KQGTBSSR5/graph.json","fetch_events":"https://pith.science/api/pith-number/DGTZ32VCI5ROXHHI7KQGTBSSR5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DGTZ32VCI5ROXHHI7KQGTBSSR5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DGTZ32VCI5ROXHHI7KQGTBSSR5/action/storage_attestation","attest_author":"https://pith.science/pith/DGTZ32VCI5ROXHHI7KQGTBSSR5/action/author_attestation","sign_citation":"https://pith.science/pith/DGTZ32VCI5ROXHHI7KQGTBSSR5/action/citation_signature","submit_replication":"https://pith.science/pith/DGTZ32VCI5ROXHHI7KQGTBSSR5/action/replication_record"}},"created_at":"2026-05-18T04:40:56.482797+00:00","updated_at":"2026-05-18T04:40:56.482797+00:00"}